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Simplifying 0 = 5x2 + -55x + 25 Reorder the terms: 0 = 25 + -55x + 5x2 Solving 0 = 25 + -55x + 5x2 Solving for variable 'x'. Combine like terms: 0 + -25 = -25 -25 + 55x + -5x2 = 25 + -55x + 5x2 + -25 + 55x + -5x2 Reorder the terms: -25 + 55x + -5x2 = 25 + -25 + -55x + 55x + 5x2 + -5x2 Combine like terms: 25 + -25 = 0 -25 + 55x + -5x2 = 0 + -55x + 55x + 5x2 + -5x2 -25 + 55x + -5x2 = -55x + 55x + 5x2 + -5x2 Combine like terms: -55x + 55x = 0 -25 + 55x + -5x2 = 0 + 5x2 + -5x2 -25 + 55x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -25 + 55x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-5 + 11x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-5 + 11x + -1x2)' equal to zero and attempt to solve: Simplifying -5 + 11x + -1x2 = 0 Solving -5 + 11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 5 + -11x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -11x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -11x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -11x + x2 = 0 + -5 -11x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -11x + x2 = -5 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -5 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -5 + 30.25 Combine like terms: -5 + 30.25 = 25.25 30.25 + -11x + x2 = 25.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 25.25 Calculate the square root of the right side: 5.024937811 Break this problem into two subproblems by setting (x + -5.5) equal to 5.024937811 and -5.024937811.Subproblem 1
x + -5.5 = 5.024937811 Simplifying x + -5.5 = 5.024937811 Reorder the terms: -5.5 + x = 5.024937811 Solving -5.5 + x = 5.024937811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 5.024937811 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 5.024937811 + 5.5 x = 5.024937811 + 5.5 Combine like terms: 5.024937811 + 5.5 = 10.524937811 x = 10.524937811 Simplifying x = 10.524937811Subproblem 2
x + -5.5 = -5.024937811 Simplifying x + -5.5 = -5.024937811 Reorder the terms: -5.5 + x = -5.024937811 Solving -5.5 + x = -5.024937811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -5.024937811 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -5.024937811 + 5.5 x = -5.024937811 + 5.5 Combine like terms: -5.024937811 + 5.5 = 0.475062189 x = 0.475062189 Simplifying x = 0.475062189Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.524937811, 0.475062189}Solution
x = {10.524937811, 0.475062189}
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